Source: Gazette of the Australian Mathematical Society
Problem: Two people, Give and Take, divide a pile of one hundred coins between themselves as follows. Give chooses a handful of coins from the pile and Take decides who will get them. This is repeated until all coins have been taken or until one of them has taken nine handfuls. In the latter case, the other person is allowed to take all of the remaining coins in the pile. What is the largest number of coins that Give can be sure of getting?
Solution: Solution by Aaditya Ramdas (CSE, IITB alumnus & Tower Research) in comments!! Further explained by me in comments!!